Heavy-fermion Superconductor Research Articles

Observations of the effect of strong Pauli paramagnetism on the vortex lattice in superconducting CeCu2Si2

We present the results of a study of the vortex lattice in the heavy fermion superconductor ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$, using small-angle neutron scattering (SANS). In this material at temperatures well below ${T}_{\mathrm{c}}\ensuremath{\sim}0.6$ K, the value of the upper critical field ${B}_{\mathrm{c}2}\ensuremath{\sim}2.2$ T is strongly limited by the Pauli paramagnetism of the heavy fermions. In this temperature region, our SANS data show an increase in the magnetization of the flux line cores with field, followed by a rapid fall near ${B}_{\mathrm{c}2}$. This behavior is the effect of Pauli paramagnetism and we present a theory-based model, which can be used to describe this effect in a range of materials. The pairing in ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$ appears to arise from the effect of magnetic fluctuations, but the evidence for a $d$-wave order parameter is rather weak. We find that the vortex lattice structure in ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$ is close to regular hexagonal. There are no phase transitions to square or rhombic structures; such transitions are expected for $d$-wave superconductors and observed in ${\mathrm{CeCoIn}}_{5}$; however, the temperature dependence of the SANS intensity indicates that both large and small gap values are present, most likely due to multiband $s$-wave superconductivity, rather than a nodal gap structure.

Unconventional superconductivity mediated solely by isotropic electron-phonon interaction

Unconventional superconductivity is commonly linked to electronic pairing mechanisms, since it is believed that the conventional electron-phonon interaction (EPI) cannot cause sign-changing superconducting gap symmetries. Here, we show that this common understanding needs to be revised when one considers a more elaborate theory of electron-phonon superconductivity beyond standard approximations. We self-consistently solve the full-bandwidth, anisotropic Eliashberg equations including vertex corrections beyond Migdal's approximation assuming the usual isotropic EPI for cuprate, Fe-based, and heavy-fermion superconductors with nested Fermi surfaces. In the case of the high-${T}_{c}$ cuprates we find a $d$-wave order parameter, as well as a nematic state upon increased doping. For Fe-based superconductors, we obtain ${s}_{\ifmmode\pm\else\textpm\fi{}}$ gap symmetry, while for heavy-fermion ${\mathrm{CeCoIn}}_{5}$ we find unconventional $d$-wave pairing. These results provide a proof of concept that EPI cannot be excluded as a mediator of unconventional and of high-${T}_{c}$ superconductivity.

Pairing interaction in superconducting UCoGe tunable by magnetic field

The mechanism of unconventional superconductivity, such as high-temperature-cuprate, Fe-based, and heavy-fermion superconductors, has been studied as a central issue in condensed-matter physics. Spin fluctuations, instead of phonons, are considered to be responsible for the formation of Cooper pairs, and many efforts have been made to confirm this mechanism experimentally. Although a qualitative consensus seems to have been obtained, experimental confirmation has not yet been achieved. This is owing to a lack of the quantitative comparison between theory and experiments. Here, we show a semi-quantitative comparison between the superconducting-transition temperature ($T_{\rm SC}$) and spin fluctuations derived from the nuclear magnetic resonance (NMR) experiment on the ferromagnetic (FM) superconductor UCoGe, in which the FM fluctuations and superconductivity are tunable by external fields. The enhancement and abrupt suppression of $T_{\rm SC}$ by applied fields, as well as the pressure variation of $T_{\rm SC}$ around the FM criticality are well understood by the change in the FM fluctuations on the basis of the single-band spin-triplet theoretical formalism. The present comparisons strongly support the theoretical formalism of spin-fluctuation-mediated superconductivity, particularly in UCoGe.

Determining Dark-Matter-Electron Scattering Rates from the Dielectric Function.

We show that the rate for dark-matter-electron scattering in an arbitrary material is determined by an experimentally measurable quantity, the complex dielectric function, for any dark matter interaction that couples to electron density. This formulation automatically includes many-body effects, eliminates all systematic theoretical uncertainties on the electronic wave functions, and allows a direct calibration of the spectrum by electromagnetic probes such as infrared spectroscopy, x-ray scattering, and electron energy-loss spectroscopy. Our formalism applies for several common benchmark models, including spin-independent interactions through scalar and vector mediators of arbitrary mass. We discuss the consequences for standard semiconductor and superconductor targets and find that the true reach of superconductor detectors for light mediators exceeds previous estimates by several orders of magnitude, with further enhancements possible due to the low-energy tail of the plasmon. Using a heavy-fermion superconductor as an example, we show how our formulation allows a rapid and systematic investigation of novel electron scattering targets.

Photoemission signature of momentum-dependent hybridization in CeCoIn5

Hybridization between $f$ electrons and conduction bands ($c$-$f$ hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn$_5$ heavy fermion superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of $T=6$ K. The used photon energy of 122 eV corresponds to Ce $4d$-$4f$ resonance. Calculations carried out with relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining $f$-electron character when approaching Fermi energy. We have also observed a considerable variation of $f$-electron spectral weight at $E_F$, which is normally determined by both matrix element effects and wave vector dependent $c$-$f$ hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of $4f$-electron enhanced spectral intensity at $E_F$ around $\bar{\Gamma}$ and $\bar{M}$ points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of $4f$-electron density for a range of values of the parameters used in the model.

Nanoscale heterogeneity induced by nonmagnetic Zn dopants in the quantum critical metal CeCoIn5 : In115 NQR/NMR and Co59 NMR study

Antiferromagnetism in a prototypical quantum critical metal ${\mathrm{CeCoIn}}_{5}$ is known to be induced by slight substitutions of nonmagnetic Zn atoms for In. In nominally 7% Zn-substituted ${\mathrm{CeCoIn}}_{5}$, an antiferromagnetic (AFM) state coexists with heavy fermion superconductivity. Heterogeneity of the electronic states is investigated in Zn-doped ${\mathrm{CeCoIn}}_{5}$ by means of nuclear quadrupole and magnetic resonances (NQR and NMR). Site-dependent NQR relaxation rates $1/{T}_{1}$ indicate that the AFM state is locally nucleated around Zn substituents in the matrix of a heavy fermion state, and percolates through the bulk at the AFM transition temperature ${T}_{\mathrm{N}}$. At lower temperatures, an anisotropic superconducting (SC) gap below the SC transition temperature ${T}_{\mathrm{c}}$, and the SC state permeates through the AFM regions via a SC proximity effect. Applying an external magnetic field induces a spin-flop transition near 5 T, reducing the volume of the AFM regions. Consequently, a short-ranged inhomogeneous AFM state survives and coexists with a paramagnetic Fermi liquid state at high fields.

Revealing the Heavy Quasiparticles in the Heavy-Fermion Superconductor CeCu_{2}Si_{2}.

The superconducting order parameter of the first heavy-fermion superconductor CeCu_{2}Si_{2} is currently under debate. A key ingredient to understand its superconductivity and physical properties is the quasiparticle dispersion and Fermi surface, which remains elusive experimentally. Here, we present measurements from angle-resolved photoemission spectroscopy. Our results emphasize the key role played by the Ce 4f electrons for the low-temperature Fermi surface, highlighting a band-dependent conduction-f electron hybridization. In particular, we find a very heavy quasi-two-dimensional electron band near the bulk X point and moderately heavy three-dimensional hole pockets near the Z point. Comparison with theoretical calculations reveals the strong local correlation in this compound, calling for further theoretical studies. Our results provide the electronic basis to understand the heavy-fermion behavior and superconductivity; implications for the enigmatic superconductivity of this compound are also discussed.

High-energy magnetic excitations from heavy quasiparticles in CeCu2Si2

Magnetic fluctuations is the leading candidate for pairing in cuprate, iron-based, and heavy fermion superconductors. This view is challenged by the recent discovery of nodeless superconductivity in CeCu2Si2, and calls for a detailed understanding of the corresponding magnetic fluctuations. Here, we mapped out the magnetic excitations in superconducting (S-type) CeCu2Si2 using inelastic neutron scattering, finding a strongly asymmetric dispersion for E ≲ 1.5 meV, which at higher energies evolves into broad columnar magnetic excitations that extend to E ≳ 5 meV. While low-energy magnetic excitations exhibit marked three-dimensional characteristics, the high-energy magnetic excitations in CeCu2Si2 are almost two-dimensional, reminiscent of paramagnons found in cuprate and iron-based superconductors. By comparing our experimental findings with calculations in the random-phase approximation,we find that the magnetic excitations in CeCu2Si2 arise from quasiparticles associated with its heavy electron band, which are also responsible for superconductivity. Our results provide a basis for understanding magnetism and superconductivity in CeCu2Si2, and demonstrate the utility of neutron scattering in probing band renormalization in heavy fermion metals.

Spectroscopic evidence for the direct involvement of local moments in the pairing process of the heavy-fermion superconductor CeCoIn5

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, 'composite pairing' based on the cooperative two-channel Kondo effect directly involving the f-electron moments has also been proposed for some heavy fermion compounds including CeCoIn$_5$. The origin of the spin resonance peak observed in neutron scattering measurements on CeCoIn$_5$ is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. Here, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn5 over wide ranges of temperature and magnetic field. The pairing gap opens at T$_p$ ~ 5 K, well above the bulk T$_c$ = 2.3 K, and its directional dependence is consistent with d$_{x^2-y^2}$ symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T$_p$. The concomitant appearance of the pairing gap and the field-induced gaplike feature, along with its linear increase with field, indicates that the f-electron local moments are directly involved in the pairing process in CeCoIn$_5$.

Local observation of linear- T superfluid density and anomalous vortex dynamics in URu2Si2

The heavy fermion superconductor URu$_2$Si$_2$ is a candidate for chiral, time-reversal symmetry-breaking superconductivity with a nodal gap structure. Here, we microscopically visualized superconductivity and spatially inhomogeneous ferromagnetism in URu$_2$Si$_2$. We observed linear-$T$ superfluid density, consistent with d-wave pairing symmetries including chiral d-wave, but did not observe the spontaneous magnetization expected for chiral d-wave. Local vortex pinning potentials had either four- or two-fold rotational symmetries with various orientations at different locations. Taken together, these data support a nodal gap structure in URu$_2$Si$_2$ and suggest that chirality either is not present or does not lead to detectable spontaneous magnetization.

Unusual H−T phase diagram of CeRh2As2 : The role of staggered noncentrosymmetricity

Superconductivity in a crystalline lattice without inversion is subject to complex spin-orbit-coupling effects, which can lead to mixed-parity pairing and an unusual magnetic response. In this study, the properties of a layered superconductor with alternating Rashba spin-orbit coupling in the stacking of layers, hence (globally) possessing a center of inversion, is analyzed in an applied magnetic field, using a generalized Ginzburg-Landau model. The superconducting order parameter consists of an even- and an odd-parity pairing component which exchange their roles as dominant pairing channel upon increasing the magnetic field. This leads to an unusual kink feature in the upper critical field and a first-order phase transition within the mixed phase. We investigate various signatures of this internal phase transition. The physics we discuss here could explain the recently found $H$--$T$ phase diagram of the heavy Fermion superconductor CeRh$_2$As$_2$.

Anomalous anisotropy of the lower critical field and Meissner effect in UTe2

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.

Strain driven emergence of topological non-triviality in YPdBi thin films

Half-Heusler compounds exhibit a remarkable variety of emergent properties such as heavy-fermion behaviour, unconventional superconductivity and magnetism. Several of these compounds have been predicted to host topologically non-trivial electronic structures. Remarkably, recent theoretical studies have indicated the possibility to induce non-trivial topological surface states in an otherwise trivial half-Heusler system by strain engineering. Here, using magneto-transport measurements and first principles DFT-based simulations, we demonstrate topological surface states on strained [110] oriented thin films of YPdBi grown on (100) MgO. These topological surface states arise in an otherwise trivial semi-metal purely driven by strain. Furthermore, we observe the onset of superconductivity in these strained films highlighting the possibility of engineering a topological superconducting state. Our results demonstrate the critical role played by strain in engineering novel topological states in thin film systems for developing next-generation spintronic devices.

Distinct Kondo Screening Behaviors in Heavy Fermion Filled Skutterudites with 4f^{1} and 4f^{2} Configurations.

CeOs_{4}Sb_{12} (COS) and PrOs_{4}Sb_{12} (POS) are two representative compounds that provide the ideal vantage point to systematically study the physics of multi-f-electron systems. COS with Ce 4f^{1}, and POS with Pr 4f^{2} configurations show distinct properties of Kondo insulating and heavy fermion superconductivity, respectively. We unveiled the underlying microscopic origin by angle-resolved photoemission spectroscopy studies. Their eV-scale band structure matches well, representing the common characters of conduction electrons in ROs_{4}Sb_{12} systems (R=rare earth). However, f electrons interact differently with conduction electrons in COS and POS. Strong hybridization between conduction electrons and f electrons is observed in COS with band dependent hybridization gaps, and the development of a Kondo insulating state is directly revealed. Although the ground state of POS is a singlet, finite but incoherent hybridization exists, which can be explained by the Kondo scattering with the thermally excited triplet crystalline electric field state. Our results help us to understand the intriguing properties in COS and POS, and provide a clean demonstration of the microscopic differences in heavy fermion systems with 4f^{1} and 4f^{2} configurations.

Renormalized quasiparticles, topological monopoles, and superconducting line nodes in heavy-fermion CeTX3 compounds

Non-centrosymmetric superconductors have recently attracted much attention, since the lack of inversion symmetry mixes spin singlet and triplet pairing states, which may allow the realization of topological superconductivity. In this work, we study the electronic properties of the family of inversion-broken CeTX$_3$ heavy-fermion superconductors, finding topological nodal lines as well as Dirac and Weyl points, which are renormalized closer to the Fermi energy by correlations. We find that the Weyl nodal lines have a substantial effect on the Fermi surface spin structure of the normal state, and lead to line nodes in the superconducting phase.

High-pressure phase diagrams of FeSe1\u2212xTex: correlation between suppressed nematicity and enhanced superconductivity

The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe1−xSx superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe1−xTex. When Te composition x(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to x(Te) ≈ 0.5. In contrast to FeSe1−xSx, enhanced superconductivity in FeSe1−xTex does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.

Multiorbital singlet pairing and d\u2009+\u2009d superconductivity

Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple s- and d-wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the sτ3 multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a d + d intra- and inter-band pairing, is shown to contrast with the more familiar d + id state in a way analogous to how the B- triplet pairing phase of 3He superfluid differs from its A- phase counterpart. In addition, we construct an analog of the sτ3 pairing for the heavy-fermion superconductor CeCu2Si2, using degrees-of-freedom that incorporate spin-orbit coupling. Our results lead to the proposition that d-wave superconductors in correlated multiband systems will generically have a fully-gapped Fermi surface when they are examined at sufficiently low energies.

Theoretical progress and material studies of heavy fermion superconductors

Heavy fermion superconductors belong to a special class of strongly correlated systems and unconventional superconductors. The emergence of superconductivity in these materials is closely associated with the presence of quantum critical fluctuations. Heavy fermion superconductors of different structures often exhibit distinct competing orders and superconducting phase diagrams, implying sensitive dependence of their electronic structures and pairing mechanism on the crystal symmetry. Here we give a brief introduction on recent theoretical and experimental progress in several different material families. We develop a new phenomenological framework of superconductivity combining the Eliashberg theory, a phenomenological form of quantum critical fluctuations, and strongly correlated band structure calculations for real materials. Our theory provides a unified way for systematic understanding of various heavy fermion superconductors.

Spin fluctuations and uncoventional superconducting pairing

High-<i>T</i><sub>c</sub> cuprates, iron-based superconductors, heavy-fermion superconductors and <i>κ</i>-type layered organic superconductors share some common features − the proximity of the superconducting state to the magnetic ordered state and the non-<i>s</i>-wave superconducting pairing function. It is generally believed that the Cooper pairings in these unconventional superconductors are mediated by spin fluctuations. In this paper, we present a brief overview on the spin dynamics and unconventional pairing, focusing on high-<i>T</i><sub>c</sub> cuprates and iron-based superconductors. In particular, we will overview the properties of the neutron spin resonance and its possible origin, the pairing mechanism in Hubbard model within the weak-coupling framework and its application to the aforesaid unconventional superconductors. We point out that the interplay between magnetism and superconductivity is still an area of active research.

Theory of (s+id) pairing in mixed-valent correlated metals

Motivated by the recent discovery of superconductivity in square-planar nickelates as well as by longstanding puzzling experiments in heavy-fermion superconductors, we study Cooper pairing between correlated $d$-electrons coupled to a band of weakly-correlated electrons. We perform self-consistent large N calculations on an effective $t-J$ model for the $d$-electrons with additional hybridization. Unlike previous studies of mixed-valent systems, we focus on parameter regimes where both hybridized bands are relevant to determining the pairing symmetry. For sufficiently strong hybridization, we find a robust $s+id$ pairing which breaks time-reversal and point-group symmetries in the mixed-valent regime. Our results illustrate how intrinsically multi-band systems such as heavy-fermions can support a number of highly non-trivial pairing states. They also provide a putative microscopic realization of previous phenomenological proposals of $s+id$ pairing and suggest a potential resolution to puzzling experiments in heavy-fermion superconductors such as U$_{1-x}$Th$_x$Be$_{13}$ which exhibit two superconducting phase transitions and a full gap at lower temperatures.